Talk:Intrinsic equation

Image?

there's an example image at Intrinsic_coordinates.png which is currently linked to by nothing! I tried to add it but it ended up too big and I don't know how to format it, maybe someone who knows syntax could help? Thanks. —Preceding unsigned comment added by 94.192.127.152 (talk) 21:42, 10 April 2011 (UTC)

The formulae look a bit messy - instead of using the square root cubed, would it be better to go for a single exponent of 3/2? - Drw25 14:43, 20 Feb 2005 (UTC)

• Yeah, I tried to do that but I couldn't get LaTeX to do it... LukeSurl 21:57, 21 Feb 2005 (UTC)
  • Sorted. If you want a power consisting of more than one character, you have to enclose the power in braces: { }. Hammerite

I changed uppercase psi to lowercase psi because I'm pretty sure it is the standard notation. 82.32.8.175 19:54, 22 May 2006 (UTC)

Not a true coordinate system?

Generally, a coordinate system is a means by which an arbitrary point in the plane or space can be identified. This isn't true of intrinsic coordinates: points outside of the curve have no (s, ψ) coordinates, and different intrinsic equations can lead to the same (s, ψ) being in completely different places relative to the s = 0 point.

This doesn't seem to make sense: "it may break down entirely when straight lines are considered". This is no more true than it is that Cartesian coordinates may break down when you consider vertical lines. Just as a vertical line in Cartesian coordinates is x = k, so a straight line in intrinsic coordinates is ψ = k.

Moreover, why s = f(ψ)? ψ = f(s) is much more general. -- Smjg 15:59, 2 February 2007 (UTC)

The name of the article should be changed to 'Intrinsic equation'. Authoritative sources such as Mathworld use this and not 'Intrinsic coordinates' which, unless there is some meaning that I'm not aware of (and I've googled the phrase to see if I could find one), makes no sense.--RDBury (talk) 13:00, 13 July 2008 (UTC)

Also the article essentially defines the Whewell equation, the term intrinsic is more generic than that. I'm going to try to move the article, find some references, and make the appropriate changes. —Preceding unsigned comment added by RDBury (talk • contribs) 13:08, 13 July 2008 (UTC)

The changes were made. I tried to preserve as much of the original material as possible by merging with other articles and creating a new one. The conversion section was deleted because the it's not really possible to carry out in practice. To get an equation relating arc length and tangential angle you must find both of these quantities in terms of the parameter and then eliminate the parameter. Arc length is usually given by an integral that can't be solved in closed form and the expression for tangential angle can be complicated, so eliminating the parameter from these two equations is more or less out of the question. Try to do this with the ellipse to appreciate the difficulties involved.--RDBury (talk) 17:53, 13 July 2008 (UTC)

Once upon a time this article had some very useful reference information which has been wiped clean - is there any reason behind this?

Cte

“ The equation of a circle (including a line) for example is given by the equation $\kappa (s)=Cte$ where $s$ is the arc length and $\kappa$ the curvature. ”

And what's Cte? French constante? —Tamfang (talk) 20:53, 15 July 2011 (UTC)

At some point Cte was changed to 1/r. —Tamfang (talk) 21:09, 26 November 2023 (UTC)